Several initial boundary value problems for the linearized KdV equation are solved. These problems are formulated in the quarter plane or in a wedge shaped domain and they involve Dirichlet, Neumann as well as changing type boundary conditions. The solution, given in terms of an explicit integral representation, is obtained by using the new spectral method introduced in Fokas (1997). The extension of these results to the KdV equation is also briefly discussed.
|Number of pages
|Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
|Published - Feb 1998